RMS displacements of electrons in a two dimensional Wigner crystal

We study the quantization of the vibrations in a two dimensional Wigner crystal in the presence of a magnetic field and also under conditions of strong electron–ripplon coupling. Under these conditions we calculate the magnitude of the rms displacements of the electrons ⟨u2⟩ at the lattice sites as a function of the magnetic field strength and the temperature. Based on the results obtained we estimate the validity of the various approaches described in the literature for the determination of ⟨u2⟩.

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